Symmetries in scalar potential scattering

A plane wave is scattered by a potential of bounded support. Translation, rotation and reflection of the potential, q0 induce symmetries on the scattered wave. The latter is represented by a Born sequence, where the reference potential, q0, appears. The result is applied to derive invariance of the scattering magnitude to finite translation and reflection. Conditions on the entries of an \almost SO(3)" matrix are derived, which induce symmetries of the scattering amplitude by the first Born approximation.